Sharon travels 15 miles west and then 8 miles south. How far is she from her starting point?
15 miles
16 miles
18 miles
17 miles
To find the distance from Sharon's starting point, we can use the Pythagorean theorem.
By traveling 15 miles west and 8 miles south, we create a right triangle with the distance from the starting point as the hypotenuse. The legs of the triangle are 15 miles and 8 miles.
Using the Pythagorean theorem (a^2 + b^2 = c^2), we can find the length of the hypotenuse (c):
c^2 = 15^2 + 8^2
c^2 = 225 + 64
c^2 = 289
Taking the square root of both sides:
c = √289
c = 17
Therefore, Sharon is 17 miles from her starting point.
The root rafter of a house has been raised to a height of 18 yards at the ridge. Half of the length of the run measures 14 yards. Find the length of the rafter.
18 yards
28 yards
22.80 yards
14 yards
To find the length of the rafter, we can use the Pythagorean theorem. The Pythagorean theorem states that for a right triangle, the sum of the squares of the lengths of the two legs is equal to the square of the length of the hypotenuse.
In this case, the height of the ridge forms one leg of the right triangle and the half length of the run forms the other leg. The length of the rafter is the hypotenuse.
Let's calculate the length of the rafter using the Pythagorean theorem:
c^2 = a^2 + b^2
where c is the length of the rafter (hypotenuse) and a and b are the legs.
Given:
Height of the ridge (a) = 18 yards
Half length of the run (b) = 14 yards
c^2 = 18^2 + 14^2
c^2 = 324 + 196
c^2 = 520
Taking the square root of both sides:
c = √520
c ≈ 22.80 yards
Therefore, the length of the rafter is approximately 22.80 yards.
To find out how far Sharon is from her starting point, we can use the Pythagorean theorem. The Pythagorean theorem states that the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides in a right triangle.
In this case, we can consider Sharon's travel west and south to form the two sides of a right triangle. The distance she travels west is 15 miles, and the distance she travels south is 8 miles.
Using the Pythagorean theorem, we can calculate the distance as follows:
Distance^2 = (15 miles)^2 + (8 miles)^2
Distance^2 = 225 miles^2 + 64 miles^2
Distance^2 = 289 miles^2
Therefore, the distance is the square root of 289 miles^2, which is 17 miles.
Therefore, Sharon is 17 miles away from her starting point.